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Properties

Label 280.6.b
Level $280$
Weight $6$
Character orbit 280.b
Rep. character $\chi_{280}(141,\cdot)$
Character field $\Q$
Dimension $120$
Sturm bound $288$

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Defining parameters

Level: \( N \) \(=\) \( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 280.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Sturm bound: \(288\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(280, [\chi])\).

Total New Old
Modular forms 244 120 124
Cusp forms 236 120 116
Eisenstein series 8 0 8

Trace form

\( 120 q - 2 q^{2} + 42 q^{4} - 408 q^{6} + 196 q^{7} - 674 q^{8} - 9720 q^{9} + O(q^{10}) \) \( 120 q - 2 q^{2} + 42 q^{4} - 408 q^{6} + 196 q^{7} - 674 q^{8} - 9720 q^{9} + 100 q^{10} + 1572 q^{12} - 1078 q^{14} - 1800 q^{15} - 3310 q^{16} + 1758 q^{18} - 8808 q^{22} + 11024 q^{23} - 13300 q^{24} - 75000 q^{25} + 10148 q^{26} - 9310 q^{28} - 11600 q^{30} - 14320 q^{31} - 10482 q^{32} - 11344 q^{33} - 3320 q^{34} - 75338 q^{36} - 15620 q^{38} + 89808 q^{39} - 12400 q^{40} - 23216 q^{41} - 90508 q^{44} + 4512 q^{46} + 113196 q^{48} + 288120 q^{49} + 1250 q^{50} + 42616 q^{52} + 81004 q^{54} + 5390 q^{56} - 61616 q^{57} - 70868 q^{58} + 54900 q^{60} - 319664 q^{62} - 79380 q^{63} + 101442 q^{64} + 61116 q^{66} - 152764 q^{68} + 128392 q^{71} + 17082 q^{72} + 45192 q^{74} + 551292 q^{76} + 77676 q^{78} - 370920 q^{79} - 32000 q^{80} + 829736 q^{81} + 95092 q^{82} - 80948 q^{84} + 376884 q^{86} + 301872 q^{87} - 272484 q^{88} - 32400 q^{90} - 40960 q^{92} - 135076 q^{94} - 288800 q^{95} + 32076 q^{96} - 4802 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{6}^{\mathrm{new}}(280, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{6}^{\mathrm{old}}(280, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(280, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 2}\)